We studied the formation of trail patterns by Argentine ants exploring an empty arena. Using a novel imaging and analysis technique we estimated pheromone concentrations at all spatial positions in the experimental arena and at different times. Then we derived the response function of individual ants to pheromone concentrations by looking at correlations between concentrations and changes in speed or direction of the ants. Ants were found to turn in response to local pheromone concentrations, while their speed was largely unaffected by these concentrations. Ants did not integrate pheromone concentrations over time, with the concentration of pheromone in a 1 cm radius in front of the ant determining the turning angle. The response to pheromone was found to follow a Weber's Law, such that the difference between quantities of pheromone on the two sides of the ant divided by their sum determines the magnitude of the turning angle. This proportional response is in apparent contradiction with the well-established non-linear choice function used in the literature to model the results of binary bridge experiments in ant colonies (Deneubourg et al. 1990). However, agent based simulations implementing the Weber's Law response function led to the formation of trails and reproduced results reported in the literature. We show analytically that a sigmoidal response, analogous to that in the classical Deneubourg model for collective decision making, can be derived from the individual Weber-type response to pheromone concentrations that we have established in our experiments when directional noise around the preferred direction of movement of the ants is assumed.

The origins of large-scale spatial patterns in biology have been an important source of theoretical speculation since the pioneering work by Turing (1952) on the chemical basis of morphogenesis. Knowing how these patterns emerge and their functional role is important to our understanding of the evolution of biocomplexity and the role played by self organization. However, so far, conclusive evidence for local activation-long-range inhibition mechanisms in real biological systems has been elusive. Here a welldefined experimental and theoretical analysis of the pattern formation dynamics exhibited by clustering behavior in ant colonies is presented. These experiments and a simple mathematical model show that these colonies do indeed use this type of mechanism. All microscopic variables have been measured and provide the first evidence, to our knowledge, for this type of self-organized behavior in complex biological systems, supporting early conjectures about its role in the organization of insect societies.M any biological systems display large-scale features involving some characteristic scale that is much larger than the size of its individual components (1). These structures are observed in a broad range of systems and scales, from animal coats (2), shell patterns (3, 4), and neural structures (5) to the spatial distribution of individuals in ecosystems (6). In many cases, they reflect functionality and adaptation and in all of them, they provide clues for the underlying rules that generate them. In most cases, it is clear that the information available to individual units is gathered from a local neighborhood much smaller than the resulting structures, suggesting some type of amplification mechanism that relies on collective behavior.The first theoretical explanation of these types of structures was suggested in 1952 by Alan Turing (1,7,8). The basic mechanism at work involves local amplification of fluctuations (activation) and long-range inhibition and actually falls within a general class of mechanisms (9-12). These mechanisms have been identified in physical (13) and chemical (14) systems, in ecosystems (2, 6, 10, 15-18) and morphogenesis (2-5, 11, 19-26). In the slime mold (27, 28), the evidence is also strong. Critics have argued that a proof requires the identification and measurement of the microscopic mechanisms at work, and this is obviously a rather difficult task in biology.In this context, it was early suggested that social insects might actually use these types of mechanisms to build their nests (29,30) and produce a wide variety of spatiotemporal structures (31-34). Here we use social insects and their behavioral patterns of organization as our reference system. We follow a standard approach, using a well-defined and controlled experimental setup in which the whole set of parameters can be measured and therefore all of the microscopic rules can be identified. We show that the formation of cemeteries in ants (35-38) falls within the family of local activation-long range inhibition (LALI) processes...